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# Chapter 4

Exponential growth/decay function a(1+r)^x OR ab^x
Compound Interest Formula f(t)= a(1 + r/k)^kt
k value annually? quarterly? Monthly? Semiannually? Daily? k= 1, 4, 12, 2, 365
Annual percentage yield formula APY= (1+r/k)^k -1
Continuous Growth Formula f(x) = ae^rt
What does e mean? Eular number = abount 2.718
Long run behavior In exponential function where b> 1 x approaches infinity, f(x) approches infinity x approaches negative infinity, f(x) approaches 0
Long run behavior In exponential function where 0<b<1 x approaches infinity, f(x) approches 0 x approaches negative infinity, f(x) approaches infinity
vertical translation of exponential function y= 2^x = K
horizontal translation of exponential function y = 2^(x-h)
vertical stretch of exponential function y = af(x) a= b> 0 (no fraction)
vertical compression of exponential function y = af(x) a= 0<b<1
horizontal stretch of exponential function y = f(1/b(x)) b>0 (makes fraction)
horizontal compression of exponential function y = f(1/b(x)) 0<b<1 (makes whole number)
Reflection across x-axis of exponential function y= -f(x)
Reflection across y-axis of exponential function y= f(-x)
Exponential property of log logₐ mn = n logₐ m
Inverse property of log alogₐ x = x
Sum of logs property logₐ mn = logₐ m + logₐ n
Difference of logs property logₐ m/n = logₐ m - logₐ n
Change of base log property logb a = (log꜀ a) / (log꜀ b)
Conversion between periodic and continuous growth rate 1 + r = e^k
half life formula 1/2 = b^t or 1/2= e^rt
doubling time formula 2 = b^t or 2= e^rt
Created by: v.virgil
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